Article

The side-chain positioning problem: a semidefinite programming formulation with new rounding schemes

Authors:

Bernard Chazelle,

Carl Kingsford,

Mona SinghAuthors Info & Claims

PCK50: Proceedings of the Paris C. Kanellakis memorial workshop on Principles of computing & knowledge: Paris C. Kanellakis memorial workshop on the occasion of his 50th birthday

Pages 86 - 94

https://doi.org/10.1145/778348.778360

Published: 08 June 2003 Publication History

Abstract

Side-chain positioning is a central component of the protein structure prediction problem and has been the focus of a large body of research. The problem is NP-complete; in fact, it is even inapproximable. In practice, it is tackled by a variety of general search techniques and specialized heuristics. We investigate a new formulation of the problem as a semidefinite program. We introduce two novel rounding schemes and provide theoretical justifications for their effectiveness under various input conditions. We also present computational results on simulated data that show that our method outperforms a recently introduced linear programming approach on a wide range of inputs. Beyond the context of side-chain positioning, we are hopeful that our rounding schemes, which are very general, will be applicable elsewhere.

References

[1]

F. Alaster. Interior point methods in semidefinite programming with applications to combinatorial optimization. SIAM J. Optimization 5: 13--51, 1995.]]

[2]

N. Alon and N. Kahale. Approximating the independence number via the Ø - function. Math. Programming 80: 253--264, 1998.]]

Digital Library

[3]

E. Althaus, O. Kohlbacher, H.-P. Lenhof, and P. Müller. A combinatorial approach to protein docking with flexible side-chains. In Proceedings 4th Annual International Conference on Computational Molecular Biology pages 15--24, 2000.]]

Digital Library

[4]

M. Bower, F. Cohen, and R. Dunbrack. Sidechain prediction from a backbone-dependent rotamer library: A new tool for homology modeling. J. Mol. Biol. 267: 1268--1282, 1997.]]

[5]

B. Chazelle, C. Kingsford, and M. Singh. The combinatorial nature of the side-chain positioning problem: contrasts in theory and practice. In preparation.]]

[6]

B. Dahiyat and S. Mayo. De novo protein design: Fully automated sequence selection. Science 278: 82--87, 1997.]]

[7]

J. Desmet, M. De Maeyer, B. Hazes, and I. Lasters. "The dead end elimination" theorem and its use in protein side-chain positioning. Nature 356: 539--542, 1992.]]

[8]

J. Desmet, M. De Maeyer, and I. Lasters. "The dead end elimination" theorem as a new approach to the side-chain packing problem. In K. Merz and S. LeGrand, editors, The Protein Folding Problem and Tertiary Structure Prediction pages 307--337. Birkhauser Boston, Inc., 1994.]]

[9]

R. Dunbrack and M. Karplus. Backbone dependent rotamer library for proteins--application to side chain prediction. J. Mol. Biol. 230: 543--574, 1993.]]

[10]

O. Eriksson, Y. Zhou, and A. Elofsson. Side chain-positioning as an integer programming problem. In Proceedings of 1st Workshop on Algorithms in BioInformatics BRICS, University of Aarhus, Denmark, Aug. 2001.]]

Digital Library

[11]

U. Feige and K. Kilian. Heuristics for finding large independent sets, with applications to coloring semi-random graphs. In Proceedings of the 39th Annual IEEE Symp. Found. Comput. Sci. pages 674--683, 1998.]]

Digital Library

[12]

R. Fourer, D. Gay, and B. Kernighan. AMPL: A Modeling Language for Mathematical Programming Duxbury Press /Brooks/Cole Publishing Company, 2002.]]

[13]

K. Fujisawa, M. Fukuda, M. Kojima, and K. Nakata. Numerical evaluation of sdpa. Technical Report B-330, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152, Sept. 1997.]]

[14]

M. Goemans and D. Williamson. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42: 1115--1145, 1995.]]

Digital Library

[15]

R. Goldstein. Efficient rotamer elimination applied to protein side-chains and related spin glasses. Biophysical Journal 66: 1335--1340, 1994.]]

[16]

D. Gordon and S. Mayo. Radical performance enhancements for combinatorial optimization algorithms based on the dead-end elimination theorem. J. Comput. Chemistry 19: 1505--1514, 1998.]]

[17]

M. Grötschel, L. Lovász, and A. Schrijver. Geometric Algorithms and Combinatorial Optimization Springer-Verlag, Berlin, 1988.]]

[18]

ILOG CPLEX 7.1 http://www.cplex.com/]]

[19]

D. Karger, R. Motwani, and M. Sudan. Approximate graph coloring by semidefinite programming. J. ACM 45: 246--265, 1998.]]

Digital Library

[20]

I. Lasters, M. De Maeyer, and J. Desmet. Enhanced dead-end elimination in the search for the global minimum energy conformation of a collection of protein side chains. Protein Engineering 8: 815--822, 1995.]]

[21]

A. Leach and A. Lemon. Exploring the conformational space of protein side chains using dead-end elimination and the A* algorithm. Proteins 33: 227--239, 1998.]]

[22]

C. Lee. Predicting protein mutant energetics by self-consistent ensemble optimization. J. Mol. Biol. 236: 918--939, 1994.]]

[23]

C. Lee and S. Subbiah. J. Mol. Biol. 217: 373--388, 1991.]]

[24]

L. Lovász. The shannon capacity of a graph. IEEE Trans. Inform. Theory 25: 1--7, 1979.]]

[25]

Y. Nesterov and A. Nemirovsky. Interior Point Polynomial Methods in Convex Programming: Theory and Algorithms SIAM, Philadelphia, 1993.]]

[26]

N. A. Pierce and E. Winfree. Protein design is NP-hard. Prot. Eng. 15(10): 779--782, 2002.]]

[27]

J. Ponder and F. Richards. Tertiary templates for proteins: use of packing criteria in the enumeration of allowed sequences for different structural classes. J. Mol. Biol. 193: 775--791, 1987.]]

[28]

P. Raghavan and C. Thompson. Randomized rounding: a technique for provably good algorithms and algorithmic proofs. Combinatorica 7: 365--374, 1987.]]

Digital Library

[29]

J. D. P. Rolim, and L. Trevisan. A case study of de-randomization methods for combinatorial approximation problems. Journal of Combinatorial Optimization 2(3): 219--236, 1998.]]

[30]

E. Seneta. Non-negative Matrices and Markov Chains Springer-Verlag, New York, 2nd edition, 1981.]]

[31]

L. Vandenberghe and S. Boyd. Semidefinite programming. SIAM Review 38: 49--95, 1996.]]

Digital Library

[32]

Z. Zwick. Outward rotations: a tool for rounding solutions of semidefinite programming relaxations, with applications to MAX CUT and other problems. In Proceedings of the 31st Annual ACM Symposium on Theory of Computing pages 679--687, 1999.]]

Digital Library

Cited By

Ryu JLee MCha JSong CKim D(2014)BetaSCP2: A Program for the Optimal Prediction of Side-Chains in ProteinsMathematical Software – ICMS 201410.1007/978-3-662-44199-2_52(333-340)Online publication date: 2014
https://doi.org/10.1007/978-3-662-44199-2_52
Ryu JKim D(2013)Protein structure optimization by side-chain positioning via beta-complexJournal of Global Optimization10.1007/s10898-012-9886-357:1(217-250)Online publication date: 1-Sep-2013
https://dl.acm.org/doi/10.1007/s10898-012-9886-3
Łukasiak PBłażewicz JMiłostan M(2009)Some operations research methods for analyzing protein sequences and structuresAnnals of Operations Research10.1007/s10479-009-0652-y175:1(9-35)Online publication date: 5-Nov-2009
https://doi.org/10.1007/s10479-009-0652-y
Show More Cited By

Index Terms

The side-chain positioning problem: a semidefinite programming formulation with new rounding schemes
1. Applied computing
  1. Life and medical sciences
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Conferences

PCK50: Proceedings of the Paris C. Kanellakis memorial workshop on Principles of computing & knowledge: Paris C. Kanellakis memorial workshop on the occasion of his 50th birthday

June 2003

116 pages

ISBN:1581136048

DOI:10.1145/778348

Conference Chairs:
Dina Q. Goldin
University of Connecticut, Storrs, CT
,
Alex A. Shvartsman
University of Connecticut, Storrs, CT
,
Scott A. Smolka
SUNY Stony Brook, NY
,
Jeffrey S. Vitter
Purdue University, West Lafayette, IN
,
Stan B. Zdonik
Brown University, Providence, RI

Copyright © 2003 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 08 June 2003

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PCK50: Principles of Computing Knowledge: Paris C. Kanellakis Memorial Workshop

June 8, 2003

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Cited By

Ryu JLee MCha JSong CKim D(2014)BetaSCP2: A Program for the Optimal Prediction of Side-Chains in ProteinsMathematical Software – ICMS 201410.1007/978-3-662-44199-2_52(333-340)Online publication date: 2014
https://doi.org/10.1007/978-3-662-44199-2_52
Ryu JKim D(2013)Protein structure optimization by side-chain positioning via beta-complexJournal of Global Optimization10.1007/s10898-012-9886-357:1(217-250)Online publication date: 1-Sep-2013
https://dl.acm.org/doi/10.1007/s10898-012-9886-3
Łukasiak PBłażewicz JMiłostan M(2009)Some operations research methods for analyzing protein sequences and structuresAnnals of Operations Research10.1007/s10479-009-0652-y175:1(9-35)Online publication date: 5-Nov-2009
https://doi.org/10.1007/s10479-009-0652-y
Kingsford CChazelle BSingh M(2005)Solving and analyzing side-chain positioning problems using linear and integer programmingBioinformatics10.1093/bioinformatics/bti14421:7(1028-1039)Online publication date: 1-Apr-2005
https://dl.acm.org/doi/10.1093/bioinformatics/bti144
Bahadur KAkutsu TTomita ESeki T(2004)Protein side-chain packing problemProceedings of the second conference on Asia-Pacific bioinformatics - Volume 2910.5555/976520.976546(191-200)Online publication date: 1-Jan-2004
https://dl.acm.org/doi/10.5555/976520.976546

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